Related papers: Is 2NF a Stable Normal Form?

An \itbf{indeterminate string} (or, more simply, just a \itbf{string}) $\s{x} = \s{x}[1..n]$ on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$. We say that $\s{x}[i_1]$ and $\s{x}[i_2]$ \itbf{match} (written $\s{x}[i_1]…

A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…

The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…

Halls of Fame are fascinating constructs. They represent the elite of an often very large amount of entities---persons, companies, products, countries etc. Beyond their practical use as static rankings, changes to them are particularly…

Deep tabular modelling increasingly relies on in-context learning where, during inference, a model receives a set of $(x,y)$ pairs as context and predicts labels for new inputs without weight updates. We challenge the prevailing view that…

Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function. AlgNNs provide a generalization of…

We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…

Several `edge-discovery' applications over graph-based data models are known to have worst-case quadratic time complexity in the nodes, even if the discovered edges are sparse. One example is the generic link discovery problem between two…

This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra…

We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting…

We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…

In Convolutional Neural Network (CNN) based image processing, most of the studies propose networks that are optimized for a single-level (or a single-objective); thus, they underperform on other levels and must be retrained for delivery of…

While the deployment of neural networks, yielding impressive results, becomes more prevalent in various applications, their interpretability and understanding remain a critical challenge. Network inversion, a technique that aims to…

Ranking is a central task in machine learning and information retrieval. In this task, it is especially important to present the user with a slate of items that is appealing as a whole. This in turn requires taking into account interactions…

Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…

Relational databases are among the most widely used architectures to store massive amounts of data in the modern world. However, there is a barrier between these databases and the average user. The user often lacks the knowledge of a query…

Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…

Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of…

Most enterprise data is distributed in multiple relational databases with expert-designed schema. Using traditional single-table machine learning techniques over such data not only incur a computational penalty for converting to a 'flat'…

Dependency parsing is the task of inferring natural language structure, often approached by modeling word interactions via attention through biaffine scoring. This mechanism works like self-attention in Transformers, where scores are…